If the mutant fish is false (ie has less than 5 truths) then one of the two fin cells at r9c12 must be true. If the fish is true then all fin and spot cells are false which leads to (7)r4c3 being true too.Thus r9c3 is false which makes this fish false too.

My take on this is that the construction of the base and cover sets is perfectly valid as each house in both sets holds at least one fish cell, and it is only because some other cells have already been eliminated that it can't be true. However once the elimination of r9c3 is made, box 7 no longer holds a fish cell and the fish becomes invalid.

From my puritanical standpoint a fish pattern should only consist of the cells in the two constraint sets and nothing more. This elimination depends on the external cell r5c2 being empty which consequently must be linked to the fish using an AIC. It then ceases to be a purely fish-based elimination. On these grounds I suspect most, if not all, remotely finned fish patterns would also fail.

[Edit] r5c3 corrected to r5c2

Last edited by David P Bird on Sun Jul 04, 2010 8:49 am, edited 1 time in total.

Like the one I posted before, this AIC uses external constraints such as b2 & r4, so it also fails my "pure fish" exclusion test.

I don't understand your No-fish solution though. The 5Fish you give is valid in my book as each constraint holds a body cell and it's only the contents of external cells that make it impossible in practice.My first problem is that r6c12 are marked as if they are body cells but I take them to be fins and so they would also be guardians.My second problem is that I don't think proving the fish must be false can be done using a linear inference chain. It either requires a net based approach and/or splitting out a sub-puzzle assuming all spot and fin cells are false which amounts to bifurcation â€“ two techniques I refuse to allow myself.

Perhaps permitting split group nodes is a lesser evil than having to resort to mutant fish! They verge on using nets but there's an important difference in that while parallel inferences are being followed, they must stay in step.

TAGdpbSplitNodes

[edit] diagram and TAG added

Last edited by David P Bird on Thu Jun 02, 2016 2:15 pm, edited 1 time in total.

Thanks to all for the responses. Here are my favorites. The jellyfish is a different outlook on JC Van Hay's "pure net solution." The starfish is an adaptation of daj95376's deduction here. The whale is an exact replica of JC Van Hay's "fish solution."

Note that the smaller the fish, the larger the quantity of remote fins. The jellyfish has two remote fins, the starfish has one and the whale has none. Note also that the chains for the remote fins use only the defining base sets for the fish.

Comments: My "Is this a Fish or NoFish?" question was misleading. I meant the move was to be considered NoFish only if a valid Fish did not exist. My GFF program does not find the whale above, so I'm off bug-hunting.

David P Bird, As stated earlier, I was unable to make your fish work in Xsudo. Subsequent retries were also unsuccessful.

None of what I did depends on knowing if the forced candidate is true or false. I added the comment "and it's not" to highlight that my X-chain was based on a false premise leading to the elimination. I though this was more noteworthy than starting from a true premise and reaching the elimination.

That said, you might note that the Jellyfish has only two fin cells ... and both of them are peers to the elimination cell. The only exception to a traditional GFF solution is that the unfinned fish pattern doesn't include the elimination cell as a PE. What's needed to complete the process is that the candidate grid doesn't support all of the vertices of the unfinned fish pattern ... and applying the unfinned fish eliminations leads to the (subsequently incorrectly) forced cell leading to the desired elimination.

If any fin cell is true then the body cells can't hold a truth in the same base constraint and the fish would be false as it couldn't hold 5 truths. This is the basis of the opening strong inference

(7)r9c12 = (7)5Fish:r4c6b137\r126c37

If each of the 5 constraints in the base and cover sets is satisfied by a body cell, then no other fin or spot cell can be true. This is the basis for the following weak inference where the second node consists of one fin and one spot cell.

(7)5Fish:r4c6b137\r126c37 - (7)r69c2

The rest of the elimination comes from just following alternating inferences.

That's why I object to focussing only on the non-body cells in the cover set as "Potential Eliminations" and ignoring their equivalence to fin cells.

As for favourites, mine is the final one I posted using the finned X-wing and split group nodes.

PS As can be seen, I've been playing with my grid template. It displays well with Internet Explorer, but please let me know if it doesn't on any other browser.

[edit] Grid changed - sorry I originally pasted the wrong one out of my collection.

Last edited by David P Bird on Mon Jul 05, 2010 10:16 pm, edited 1 time in total.